On central automorphisms of finite p-groups

TL;DR

This paper characterizes finite p-groups of small order where the center of the inner automorphism group equals the group of central automorphisms, providing a detailed classification for these groups.

Contribution

It offers a complete characterization of such p-groups for orders up to p^6, extending previous understanding of automorphism groups in finite p-groups.

Findings

Identifies all p-groups of order p^n (n ≤ 6) with the specified automorphism property.

Provides explicit descriptions for groups of order p^5 and p^6.

Extends known classifications to include cases with odd primes for n=6.

Abstract

We characterize all finite p-groups G of order p^n(n\leq 6), where p is a prime for n\leq 5 and an odd prime for n = 6, such that the center of the inner automorphism group of G is equal to the group of central automorphisms of G.